Monday, October 5, 2015

Math Tip Monday: Addition & Subtraction Basics

Welcome back to Math Tip Monday. Once again, I am teaming up with K's Classroom Kreations to bring you a blog hop full of great ideas for teaching math. This month's topic: Addition and Subtraction Basics. After giving it some thought, I decided to share with you three ideas that I've found extremely helpful in my classroom.

Math Talks

Several years ago, I discovered a resource that began to transform my mathematics teaching. The book, Teaching Student Centered Mathematics Grades K-3 by John A. Van de Walle and LouAnn Lovin, helped me to see that the old model of teacher directed instruction (direct instruction, guided practice, and independent practice) did not help students to construct their own understanding of concepts. As a constructivist in my literacy instruction, I found the practices suggested in this book more closely matched my philosophy of teaching than traditional mathematics instruction.

Van de Walle suggests creating a "mathematical community of learners." I've shared how I do that in a previous post. He suggests that "classroom discussion based on students' own ideas and solutions to problems" is a critical component of the mathematics classroom. Well, math talks provide a forum for students to share ideas about their thinking and learning with their peers.

Van de Walle also advises that instruction that is based on problem-solving engages students and helps them to make sense of ideas. Math talks allow students to discuss ideas about concepts, strategies, and barriers to problem solving. They are a great way to teach students how to choose effective strategies for addition and subtraction. They are also great for helping students to use mistakes as tools for learning. Finding the right answer is never the goal of a math talk. Instead, the class focuses on understanding real-life problems and finding effective and reliable strategies for solving them.

So how does a math talk work in my classroom?
First we have to establish the expectations for the math talk. After we've started to come together as a classroom community, I gather the students together on the carpet and tell them about math talks. Since we are all mathematicians, we can all help each other learn math. I tell them that when we have a math talk, we will work together to understand a problem and share ideas for how to solve it. I ask them what we should do to help each other learn. Together, we create an anchor chart like this one.

Our first few math talks usually focus more on practicing the expectations than solving the problems themselves. Once we've got an established procedure, a math talk might go like this.

I bring students to the carpet with their math journals and a pencil. I share a slide that has one problem posted on it.

We read the problem together once. Then I ask students to visualize as we read the problem a second time, one sentence at a time. I then ask a student to restate the problem, (i.e. Johnny, what's going on in this problem?). I ask guiding questions such as,

So what do we need to do?

How do you know?

Are you sure it's addition/subtraction? Why?

What would be a good strategy to use to solve this problem?

What is another strategy we could use?

Once we've discussed the problem, students work to solve the problem in their math journals. After a couple of minutes, I choose two or three students to share their strategies. Here are some my students used:

I keep sharing limited to two or three students. Otherwise, the math talk can drag on too long.

After sharing our strategies, I then briefly review our learning about the problem and end the talk. From beginning to end, the math talk should take about 10 minutes.

Here are some common problems that have come up during our math talks and how I've solved them.

Problem:Students begin to solve the problem before you've discussed it as a class.

Solution: Have students place closed journals and pencils behind them on the carpet. I've even had students sit on their journals until we are ready to solve.

Problem: Students blurt out the answer before you've analyzed the problem.

Solution:Either acknowledge it or ignore it. Students gradually come to realize that the answer is not the most important part of a math talk. If you choose to acknowledge it and the student has the correct answer, you can simply say, "Yes, the answer is 23, but as mathematicians, we need to understand how we get the answer." Then redirect to the question at hand, "So how did you know that you needed to add?"

Problem:The same students participate all the time and others seem disengaged.

Solution: Use cold calling or a bucket of names to randomize student participation. If students know they might be called on at any time, they are more likely to be prepared. Refer to the anchor chart to remind students that all mathematicians participate in the math talk.

Problem:The math talk drags on too long.

Solution: Decide what to focus on before the math talk. Spend more time on that. For example, if you want students to understand different strategies for subtraction, spend less time analyzing the problem and more time discussing the strategies. You may need to draw or record the strategies if time is running short. Just ask students to tell you what to write. Keep the pace moving. Set a timer if necessary. Your students will tune out after ten minutes, so you really don't want this part of your lesson to take too long.

Strategy Board

A strategy board is a great resource that has really helped my students. As we learn new strategies for addition or subtraction, we add it to our board. The board stays up in our room. When students are stuck, I often refer to the board. Choosing a strategy helps them to get started. Here's one that I've made. Yours can be as fancy or as basic as you like. Use whatever works for you.

Fact Fluency Practice using Math Games

In my school, second graders are expected to be fluent with addition and subtraction facts to twenty. While to some this might mean memorization, to me that means students have become so efficient with their mental math strategies that they are quickly and easily able to solve these problems with accuracy.

One of the ways that students gain this proficiency is they have multiple opportunities to practice these facts. While flashcards can be useful, especially when you make a game out of it, I've found that games provide students with multiple opportunities to practice facts in a fun and meaningful way. Luckily, the math program we use, Investigations, emphasizes the use of math games to practice fluency. While I can't share their copyrighted games with you, here are a few others that I've used.

Fast Facts:
In this game, students use a timer and a pair of number dice to practice facts with a partner. The partner turns over or starts the timer, says when to start and stop, and checks the answers. The player begins rolling the dice and adding the digits, writing only the answers in his/her math journal. Once time is up, both partners count how many problems were successfully solved. Then, partners switch roles. This is a great activity for early finishers.

Flash Card War:
This game is based on the classic card game, War. The students divide the flash cards evenly among each player. Each player turns over the flash card on the top of their pile and places it in the center of the group, Players add their own cards. The player with the greatest sum collects all cards played. If players have sums of equal amounts, there is a "war." Saying, "I declare WAR!" each student places three more cards, then adds the last one placed. The player with the greatest sum collects all cards played in the round. Play continues until time is up or players run out of cards. The player with the most cards at the end of the game wins. Note: You can also play this game for subtraction. Just have students who have the smallest difference win the round.

Domino Addition:
Use dominoes to play a variety of addition games. They can be a simple as having students try to match dominoes that have the same sum. You can also have them create an addition "train," each time they add a domino they add the pips on the touching sides of the dominoes.

Invent a Game:
This is a great way to challenge your high-achieving math students or to involve all students in being creative mathematicians. Ask them to work together to invent a game that helps them to practice their facts. They need to use materials that are in the classroom such as dice, cards, counters, or dominoes. They need to play the game with a partner to make sure it works. Finally, they need to write the rules and directions so someone else can play. You'll be amazed at what your students come up with!

There you have it. My ideas for teaching basic addition and subtraction in your classroom. I hope some of these will be useful to you. Don't forget to check out the other great ideas from my fellow bloggers below.